Washington (CNN) -- Senate leaders from both political parties have agreed to hold a vote on legislation repealing President Obama's health care overhaul -- a top priority of GOP congressional leaders.

The vote probably will come either Tuesday or Wednesday.

The Republican-controlled House of Representatives has already passed a bill repealing the health care overhaul. Such a measure, however, has virtually no chance of winning approval in the Democratic-controlled Senate.

Senate Majority Leader Harry Reid, D-Nevada, said he wanted to get the repeal effort "out of the system" so the Senate could move ahead with other business. While all 47 Senate Republicans are expected to back a full repeal, the plan will not receive enough votes to clear the measure.

"It would be a dereliction of duty if Republicans didn't fight for repeal," said Senate Minority Leader Mitch McConnell, R-Kentucky. "We made a promise to our constituents that we would vote to repeal this bill on their behalf. And that's just what we intend to do."

Senate Democrats are expected to join Republicans in voting for the elimination of a rule, scheduled to take effect in 2012, requiring businesses to issue 1099 tax forms to any individual or corporation from which they buy more than $600 in goods or services in a year. Most liberals and conservatives view the rule as an unnecessary burden on private-sector employers.

The push for an outright repeal is one of several strategies the GOP leadership is using to undermine support for the law. Senate Republicans also introduced legislation Tuesday that would allow states to opt out of key provisions of the new health care law.

Specifically, the bill would allow state governments to opt out of the so-called individual mandate requiring everyone to obtain health care coverage by 2014 or face penalties. It would also allow states to ignore new mandates regarding employer-based coverage, insurance benefits and an expansion of Medicaid.

The measure was introduced one day after a federal judge in Florida issued a sweeping ruling against the law, siding with 26 states that had challenged the measure and setting up a likely Supreme Court challenge in the months ahead.

A federal judge in eastern Virginia has also found the health care law unconstitutional, while two other federal judges -- one in western Virginia and one in Michigan -- have ruled just the opposite. Twelve other federal judges have dismissed challenges to the law, according to the White House.

Washington "seems more out of touch than ever," said Sen. John Barrasso, R-Wyoming. The GOP bill "provides a path to freedom for our states" by letting them escape a plan "that will ultimately bankrupt them."

Our No. 1 goal is still "to repeal and replace this health care law," he said.

This new bill "takes the fight from Washington to each state," added Sen. Lindsey Graham, R-South Carolina. "This will be an issue for the 2012 election cycle."

Graham predicted that Democratic governors in large industrial states would eventually join Republicans in opposing the new law as they start to grapple with mandates imposed by the measure's Medicaid expansion.

Some leading Democrats have characterized Republican lawmakers as hypocrites for accepting government-provided health care benefits while opposing the health care overhaul, which is designed to extend coverage to millions of uninsured Americans.